addition & subtraction 4.nsbt.4 fluently add and subtract multi- digit whole numbers using...

Addition & Subtraction

4.NSBT.4 Fluently add and subtract multi-digit whole numbers using strategies to

include a standard algorithm.

What do I have to do?

• 4.NSBT.4 Fluently add and subtract multi-digit whole numbers using strategies to include a standard algorithm.• Add whole numbers with 1, 2, 3, 4, 5, or 6 digits• Subtract whole numbers with 1, 2, 3, 4, 5, or 6 digits• Illustrate and explain how you got your answer• Borrow and Regroup as needed

4-3 Adding - Review

• Make numbers bigger by combining values• Whole numbers are not fractions, decimals, or

parts• Regrouping happens when a total at a place value is

greater than 9 – also known as carrying

• I DO – MODEL:• 12,456 + 991 =

WE DO - Try this!

• Add the following numbers. Does it matter how you write them? Can you estimate what the answer will be?• 12 + 15 =• 425 + 20 =• 1,153 + 99 =• 8,465 + 111 =• 12,845 + 4,581 =• 548,364 + 23,984 =

WE DO - Try this! ANSWERS• Did it matter how you wrote them? Did you

estimate the answer? Were you close?

• 12 + 15 = 27• 425 + 20 = 445• 1,153 + 99 =1,252• 8,465 + 111 = 8,576• 12,845 + 4,581 = 17,426• 548,364 + 23,984 = 572,348

YOU DO - Practice on your own• Open your MATH WORKBOOK to Reteaching 4-3

and complete all of the problems.• If you finish early, complete Practice 4-3 as well.

• ALTERNATIVE: Pages 97-98 ALL ODD problems 1-31.

• TURN THIS IN BY THE END OF THE PERIOD

Reflect and Review

• In your math journal, write 3 sentences about how to add and when to add. Can you think of times in your everyday life that you add?

• MATH NOTES (Copy to your Math Journal)• We add when we see words like: sum, all together, in all,

total, and plus• We add when we have unequal groups and need a total• When we have more than 9 in any place value, we write

the ones digit in the sum and “carry” the tens digit

4-1 Mental Math

• Did estimating help you find an answer?• Estimating is one type of problem solving strategy

for addition and subtraction.• Estimation does not come up with an exact answer• Estimation often uses rounding numbers

• Mental math uses the things you “just know” to help you solve problems in your head

Using Mental Math to Add and Subtract

• Turn to page 90 in your math textbook and follow along, copy this into your journal

• Commutative property of addition: add numbers in the order that is EASIEST, so x + y = y + x

• Associative property of addition you can group numbers and add in any order, so (x+y)+z = x + (y+z)

• Identity property of addition means that any number plus 0 is the same number, so X + 0 = X and Y + 0 = Y

Properties of Addition – So What?• The properties of addition make when and how we

add numbers flexible!• Start with easy facts, break numbers apart, count

on or up, and compensate to solve problems• 135 + 48 is the same as 135 + 5 + 40 + 3• And the same as 135 + 40 + 5 + 3• And the same as 135 + 5 + 43• They all equal 183

I DO - Breaking Apart

• Use fact families to split up bigger numbers and GET TO 10

• Problem #1, page 91 is 86 + 25

• 86 + 25 = 80 + 6 + 20 + 1 + 4

• 86 + 4 = 90

• 90 + 21 = 90 + 10 + 11 = 111Break Apart

Break Apart

WE DO – Try this!

In your Journal:Add 97 + 15 using the “break-apart/get to 10” strategy

WE DO – Try this! Answers

97 + 15 is the same as:90 + 10 + 7 + 5= 100 + 12= 112How else can we do this?

Counting/Adding On

• Use addition to help in subtraction

• Problem # 3, page 91 is 566 - 359• 566 – 359 = 359 + X = 566• So 359 + 1 = 360• 360 + 200 = 560• 560 + 6 = 566• So 359 + 1 + 200 + 6 = 566• And 566 – 359 = 200 + 6 + 1 OR 566 – 359 = 207

X is used to represent what we DO NOT KNOW in a

problem

WE DO – Try this!

In your Journal:Subtract 122-99 using the “counting/adding on” strategy


122 - 99 is the same as:99 + X =12299 + 1 = 100100 + 22 = 12299 + 1 + 22 = 122So 99 + 23 = 122So 122 – 99 = 23

Compensation

• Compensation combines rounding and addition or subtraction to solve problems

• Problem # 5, page 91 : 239 + 509• It is really easy to add 240 + 510 = 750• Since we added 1 to each number, now we subtract

those 1’s 750 – 1 – 1 = 748• So 239 + 1 + 509 + 1 = 750 – 1 – 1 = 748

WE DO – Try this!

In your Journal:Add 157 + 61 using the “compensation” strategy


157 + 61 can be changed to: 157 + 3 + 61 =121

121 – 3 = 118

So 157 + 61 = 118

YOU DO - Practice on your own• Open your MATH TEXTBOOK to Page 91 and

complete problems 2, 4, 6, 7, 8, and 10-14 (all) ON A PIECE OF LINED PAPER, work by yourself• If you finish early, use your MATH WORKBOOK and

complete RETEACHING 4-1 and PRACTICE 4-1 as well.• After 5 minutes I will come to check on each table• TURN THIS IN BY THE END OF THE PERIOD

Reflect and Review• In your math journal, write 3 sentences about which mental

math strategies you like the best. Can you think of times in your everyday life that you use them?

•MATH NOTES (Copy to your Math Journal)• Breaking Apart, Get to 10, Counting/Adding On,

and Compensation are strategies that help us make addition and subtraction problems easy to solve in your head.

•Pack up, you may take your MATH BOOK, MATH WORKBOOK, and MATH JOURNAL home.

GAME: Rounding Relay• Each team of 4-5 players gets a whiteboard, dry-erase

marker, and eraser• A number will be called out/written on the board, one

member of each team will stand at the front of the room, the rest are at the table• One player from each team will round the number to the

nearest 10, 100, 1000, or 10,000 and hold up the board, if the answer is correct they will run back to their table and pass the board to the next player who will come back to the front• The first table/team to get all players back to their table

wins

Rounding Relay

•816•12,458•147,895•85,921•4,821

4-2 Estimating Sums and Differences• What is a sum?• What is a difference?• How does estimating help us here?• Turn to page 94 in your MATH TEXTBOOK and

follow along!

• I DO – Washington Monument Example

WE DO – Try This!

• Page 94, Problem #1 is 563 + 375• Let’s estimate!• I will round to the nearest 10, that will give me a close

answer and can even be the first step in compensation• 560 + 380 = 500 + 300 + 60 + 40 + 40 = 940• Let me see how close I was: 563 + 375 = 938• How could I have used compensation?• 563 + 2 + 375 = 940 - 2

WE DO – Try This!• Page 94, Problem #3 is 645 + 253• Let’s estimate! RAISE YOUR HAND to help!

• What place value should we round to? Why?

• What new numbers would we get?

• Let’s work the problem

YOU DO - Practice on your own• In your TEXTBOOK on pages 94 – 95, work the

following problems: ALL EVEN problems 2-30

Reflect and Review

• In your math journal, write 3 sentences about how rounding and compensation are similar and different.• MATH NOTES (Copy to your Math Journal)• When adding or subtracting we can use rounding to

estimate an answer OR to check if our answer is reasonable• The steps for rounding:

• Find the place value you need to round to• Look at the digit on the right, if it is 0-4 round down, 5-9 round up• THE PLACE VALUE you are rounding to will stay the same or go up

by 1 digit• All the digits after the place value become 0 (zero)

GAME: Rounding Relay• Each team of 4-5 players gets a whiteboard, dry-erase

marker, and eraser• A number will be called out/written on the board, one

member of each team will stand at the front of the room, the rest are at the table• One player from each team will round the number to the

nearest 10, 100, 1000, or 10,000 and hold up the board, if the answer is correct they will run back to their table and pass the board to the next player who will come back to the front• The first table/team to get all players back to their table

wins

Rounding Relay

•816•12,458•147,895•85,921•4,821

GAME: Adding Relay

• Each team of 4-5 players gets a whiteboard, dry-erase marker, and eraser, the teacher will write 5 numbers on the board• At the team’s table one player will complete an addition

problem and pass the board to the next team member who will add the next number to the original answer• The board will be passed to each teammate until all the

numbers are added• The team will receive 1 point for each correct answer and a

bonus if all the answers are correct

Adding Relay

•415 + 986• + 1,483• + 24,948• + 31• + 899

4-4 Subtraction - Review

• Subtraction reduces numbers (makes them smaller)• Subtraction can mean spending money, giving

things away, or finding the difference• Subtraction is the opposite or INVERSE of addition• Use estimation to help make sure your answer is

reasonable• Subtract from Left to Right

I DO - Subtraction• Turn to page 100 in your MATH TEXTBOOK and follow along

as I do problem #1: 527 – 338• Estimate using rounding: 530 – 340 = 190• In my head, I used compensation to estimate:• 530 + 10 – 340 = 200 – 10 = 190

• Work the problem using borrowing:• 17 – 8 = 9• 11 – 3 = 8• 4 – 3 = 1• The answer is 189• Compensation to Subtract: 527 + 1 – 338 = 190 – 1 = 189

WE DO – Try this!

• 716 – 254• How would we estimate the answer?

• Is there a strategy we should use?

• Will we have to borrow? How do you know?

• Now, let’s do 139 – 86 =

• And 1,268 – 429 =

WE DO – Try this! ANSWERS• 716 – 254 = 462• How would we estimate the answer? 720 – 260 = 460

• Is there a strategy we could use?• 700-200=500 as an estimation• 716+44-254=506-44=462

• Will we have to borrow? How do you know?• Yes, because the 5 in the tens place is greater than the 1

• 139 – 86 = 53• 1,268 – 429 = 839

YOU DO – Practice on your own • Go to pages 100-101 in your textbook, work ALL

ODD PROBLEMS 5 – 31 on a sheet of LINED PAPER

• If you finish early, go to your MATH WORKBOOK and complete the RETEACHING 4-4 and PRACTICE 4-4, all problems.

• TURN IN all COMPLETE work at the end of the period. Take your workbook and journal HOME.

Reflect and Review• In your MATH JOURNAL, write three sentences about what

your brain is thinking while you are doing subtraction by answering the following questions. • Are you able to focus? • Do you solve most of the problem in your head? • Do you have to have paper? • Is subtraction easier than addition? Why or why not?

• Math Notes: (copy into your journal)• Subtraction is the INVERSE, or opposite, of addition and shows a

DECREASE in value• Subtraction problems use words like: difference, less than, sold,

gave away, and decrease

GAME: Subtraction Relay

• Each team of 4-5 players gets a whiteboard, dry-erase marker, and eraser, the teacher will write 5 numbers on the board• At the team’s table one player will complete an addition

problem and pass the board to the next team member who will subtract the next number from the original answer• The board will be passed to each teammate until all the

numbers are subtracted• The team will receive 1 point for each correct answer and a

bonus if all the answers are correct

Subtraction Relay

•69,785 - 986• - 1,083• - 24,948• - 310• - 899

4-5 Subtracting Across Zeros• This is still subtraction, but what do you do when

there is a Zero in your way?

• Follow along in your textbook on page 102

• I DO – Page 102, Problem #1: 600-177

WE DO – Try this!• Page 102, problem # 2 is 1,086 – 728• Estimate by rounding: 1100 – 700 = 400• Use compensation: • 1,086 + 4 – 728 • 1,090 – 728 = 362 – 4 = 358• Check using addition: 728 + 358 = 1,086

• Or use regular subtraction:• 16 – 8 = 8• 7 – 2 = 5• 10 – 7 = 3

• So the answer is 358

WE DO – Try this!

• 810 – 638• How would we estimate the answer?

• Is there a strategy we should use?

• Will we have to borrow? How do you know?

• 3,304 – 1,137

• 1,001 – 868

WE DO – Try this! ANSWERS• 810 – 638• How would we estimate the answer?

• 810 – 640 OR 800-600• Is there a strategy we should use?

• Will we have to borrow? How do you know?• Yes, because we are subtracting from a 0 in the ones place

• 3,304 – 1,137 = 2,167

• 1,001 – 868 = 133

YOU DO – Practice on your own• Turn to pages 102-103 in your MATH TEXTBOOK, on

a piece of lined paper, complete problems 9-12, problems 21-24, and problems 29-34.

• If you finish early, please go to your MATH WORKBOOK and complete RETEACHING 4-5 and PRACTICE 4-5.

• Turn in ALL COMPLETED WORK at the end of the period.

Review and Reflect

• In three sentences, explain what mistakes people might commonly make when subtracting from a number that has more than 1 zero in it.

• MATH NOTES (copy into your MATH Journal)• Subtraction strategies are similar to addition

strategies. While ADDING you carry over to the next highest value(to the LEFT), when you subtract you take ten TO THE RIGHT.

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